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May/June 2009 Brezis-Merle type inequality for a weak solution to the $N$-Laplace equation in Lorentz-Zygmund spaces
Norisuke Ioku
Differential Integral Equations 22(5/6): 495-518 (May/June 2009).

Abstract

We consider a regularity estimate for a solution of the homogeneous Dirichlet problem for $N$-Laplace equations in a bounded domain $\Omega\subset{\mathbb R}^N$ with external force $f\in L^1(\Omega)$. Introducing the generalized Lorentz-Zygmund space, we show the multiple exponential integrability of the Brezis-Merle type for an entropy solution of the Dirichlet problem of the $N$-Laplace equation. We also discuss conditions on $f$ that guarantee the solutions are bounded.

Citation

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Norisuke Ioku. "Brezis-Merle type inequality for a weak solution to the $N$-Laplace equation in Lorentz-Zygmund spaces." Differential Integral Equations 22 (5/6) 495 - 518, May/June 2009.

Information

Published: May/June 2009
First available in Project Euclid: 20 December 2012

zbMATH: 1240.35209
MathSciNet: MR2501681

Subjects:
Primary: 35J92
Secondary: 35B65, 35D30, 35J25, 35J70, 46E30

Rights: Copyright © 2009 Khayyam Publishing, Inc.

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Vol.22 • No. 5/6 • May/June 2009
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